With decades of studies on matter and energy conversion in catalysis, electrochemistry, and material engineering, the importance of material surfaces and interfaces has been widely realized. The flexible tunability of morphology, composition, and local geometry by the pressure, temperature, chemical potential, and other experimental controlling methods has convinced researchers that a broad and profound understanding of phenomena at surfaces and interfaces provides new mechanisms and paradigms to solve the challenging problems people are currently facing. However, different from studies of a single phase where symmetries and isotropy can usually simply the problem, the heterogeneity of surfaces and interfaces leads to the intrinsic complexity in studies of these system. With the development of computers and theories of computational chemistry, theoretical studies through large-scale modeling and ab initio simulation have become a powerful approach to decipher the heterogeneous phenomenon. In this thesis, we present our studies in different fields to demonstrate that how theoretical studies enrich the understanding of the heterogeneous phenomena in these fields. In the field of catalysis and electrochemistry, how the reaction mechanism of the oxygen evolution reaction is modified by the hydrated surface of CaMnO3 is explained; in the field of material design and synthesis, how unstable phases can be stabilized by the substrate is presented; and in the field of matter transport, how an hierarchical nanoporous structure increases the total ion diffusion rate is proposed. In order to find stable surface reconstructions under different chemical potential, an automated searching algorithm based on the ab initio grand canonical Monte Carlo simulation is also introduced.